MinT - Information on Result #2690896

Information on Result #2690896

Linear OOA(4¹⁹⁹, 543, F₄, 3, 52) (dual of [(543, 3), 1430, 53]-NRT-code), using 4¹ times duplication based on linear OOA(4¹⁹⁸, 543, F₄, 3, 52) (dual of [(543, 3), 1431, 53]-NRT-code), using

trace code [i] based on linear OOA(64⁶⁶, 181, F₆₄, 3, 52) (dual of [(181, 3), 477, 53]-NRT-code), using
- constructionÂ X applied to AG(3;F,475P) âŠ‚ AG(3;F,483P) [i] based on
  1. linear OOA(64⁵⁹, 176, F₆₄, 3, 52) (dual of [(176, 3), 469, 53]-NRT-code), using algebraic-geometric NRT-code AG(3;F,475P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
    - a function field by GarcÃa and Quoos [i]
  2. linear OOA(64⁵¹, 176, F₆₄, 3, 44) (dual of [(176, 3), 477, 45]-NRT-code), using algebraic-geometric NRT-code AG(3;F,483P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177 (see above)
  3. linear OOA(64⁷, 5, F₆₄, 3, 7) (dual of [(5, 3), 8, 8]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(64⁷, 64, F₆₄, 3, 7) (dual of [(64, 3), 185, 8]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(3;185,64) [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

None.